Assume that F is a conservative vector field.(a) What is the definition of a vector field F being conservative? How do we check ifa vector field is conservative?(b) If things are “nice" (*all curves are simple curves in a simply connected regionD, all functions are continuously differentiable on D), what can we say about theline integrals of F over curves C1 and C2 which start and end at the same point.(c) If things are “nice," what can we say about line integrals of F over curves C1 and-C1, the same curve in the opposite direction? (Do we need to fact that F isconservative?)(d) If things are “nice," what can we say about line integrals of F over curve C whereC is a simple closed curve.

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Answered: Assume that F is a conservative vector…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 11P

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